Question

An iron spherical ball of radius 21 cm is melted and it is re-cast into small hemispheres radius 7 cm each. The number of hemispheres formed will be

• A. 54
• B. 50
• C. 52
• D. 48

Answer 1

The correct option is A

54

Given,

Radius of the spherical ball,$R=21cm$

Radius of each hemispherical ball,$r=7cm$

The volume will remain constant as same volume of iron metal is used to re-cast the hemispherical balls.

Let's assume $x$ such hemispherical balls will be formed.

So, Volume of spherical ball = $x\times$ Volume of each hemispheical ball

$\Rightarrow \frac{4}{3}\pi R^3=x\times \frac{2}{3}\pi r^3$
$\Rightarrow \frac{4}{3}\times \pi \times {21}^3=x\times \frac{2}{3}\times \pi \times 7^3$

$\Rightarrow x=54$

$\therefore$ After re-casting 54 small hemispherical balls are formed.